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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A construction of a $\lambda$-Poisson generic sequence
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by Verónica Becher and Gabriel Sac Himelfarb HTML | PDF
Math. Comp. 92 (2023), 1453-1466 Request permission

Abstract:

Years ago Zeev Rudnick defined the $\lambda$-Poisson generic sequences as the infinite sequences of symbols in a finite alphabet where the number of occurrences of long words in the initial segments follow the Poisson distribution with parameter $\lambda$. Although almost all sequences, with respect to the uniform measure, are Poisson generic, no explicit instance has yet been given. In this note we give a construction of an explicit $\lambda$-Poisson generic sequence over any alphabet and any positive $\lambda$, except for the case of the two-symbol alphabet, in which it is required that $\lambda$ be less than or equal to the natural logarithm of $2$. Since $\lambda$-Poisson genericity implies Borel normality, the constructed sequences are Borel normal. The same construction provides explicit instances of Borel normal sequences that are not $\lambda$-Poisson generic.
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Additional Information
  • Verónica Becher
  • Affiliation: Departamento de Computación, Facultad de Ciencias Exactas y Naturales & ICC, Universidad de Buenos Aires & CONICET, Argentina
  • MR Author ID: 368040
  • ORCID: 0000-0002-5425-8563
  • Email: vbecher@dc.uba.ar
  • Gabriel Sac Himelfarb
  • Affiliation: Departamento de Matemática & Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
  • ORCID: 0000-0003-1117-7023
  • Email: gabrielsachimelfarb@gmail.com
  • Received by editor(s): March 14, 2022
  • Received by editor(s) in revised form: September 19, 2022
  • Published electronically: January 31, 2023
  • Additional Notes: The second author was supported by the student fellowship “Beca de Estímulo a las Vocaciones Científicas” convocatoria 2020, Consejo Interuniversitario Nacional, Argentina. The first author was supported by Agencia Nacional de Promoción Científica y Tecnológica grant PICT-2018-02315 and by Universidad de Buenos Aires grant Ubacyt 20020170100309BA.
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 1453-1466
  • MSC (2020): Primary 11K16, 05A05, 60G55
  • DOI: https://doi.org/10.1090/mcom/3806
  • MathSciNet review: 4550334